I second this, and a directional unit like the NanoBeam will go through a simple timber wall pretty easily (but of course better if you could shoot it through a window), so you don't need to worry about mounting it outside as you seem to be concerned about routing cables to outside.
That assumes you have no significant obstruction not shown in your picture. Once the signal is received by a paired NanoBeam on your side, you can plug your PC ethernet directly into that (well, it's POE adapter), no need to install a wifi card.
You can get a pre-configured pair of NanoBeams so you just connect the ethernet cables and point them at each other.
These might do the trick.
Here is another solution from Ubiquiti that I found on Amazon:
PoE is no problem for home networking equipment, many wireless bridge units come with the injectors for power. Here's two examples of pre-configured units that would work great for you and include the PoE power injectors: one, two. Of course Amazon delivery might be weeks under current conditions. If you are trying to source something locally, there are comparable units from Ubiquiti, Mikrotik, and TP-Link.